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11Alexandr11 [23.1K]
3 years ago
8

An altitude is drawn from the vertex of an isosceles triangle, forming a right angle

Mathematics
1 answer:
Leni [432]3 years ago
6 0

Answer:

P = 63.6 inches

Step-by-step explanation:

you need to find the length of the third side:

9² + 21² = c²

81 + 441 = c²

c² = 522

c = \sqrt{522}

c ≈ 22.8

P = 18 + 2(22.8)

P = 63.6 inches

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Find a vector equation and parametric equations for the line segment that joins p to q. p(1, −1, 7), q(7, 6, 1) vector equation
AleksAgata [21]
Answers: 

- vector equation: r(t) = <1 + 6t, -1 + 7t, 7 - 6t> 
- parametric equations:   
      x = 1 + 6t
      y = -1 + 7t
      z = 7 - 6t

Explanation:

To obtain the vector equation, we first get a vector v that is parallel to the line. To get the vector v, we subtract p from q. So,

v = q - p
   = (7,6,1) - (1,-1,7)
v  = (6, 7, -6)

The vector equation of the line is given by

r(t) = v_0 + tv

Where

v_0 = a point in the line (we choose point p(1,-1,7))

So, the equation of the line joining p and q is given by

r(t) = v_0 + tv&#10;\\ \indent = \left \langle 1, -1, 7 \right \rangle + t\left \langle 6, 7, -6 \right \rangle&#10;\\ \indent = \left \langle 1, -1, 7 \right \rangle + \left \langle 6t, 7t, -6t \right \rangle&#10;\\ \indent \boxed{r(t) = \left \langle 1 + 6t, 1 + 7t, 7 - 6t \right \rangle }

In the parametric equation of the line, we just need to get the x, y and z coordinates in the vector equation.

Since the vector equation is given by 

r(t) = \left \langle 1 + 6t, 1 + 7t, 7 - 6t \right \rangle

The parametric equations of the line are given by:

x(t) = 1 + 6t&#10;\\y(t) = 1 + 7t&#10;\\z(t) =  7 - 6t


4 0
3 years ago
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